Mathematical Statistics: Basic Ideas and Selected Topics, Volume II

ISBN-13: 9781498722681 / Angielski / Twarda / 2015 / 488 str.

Kjell A. Doksum

Opis

Mathematical Statistics: Basic Ideas and Selected Topics, Volume II presents important statistical concepts, methods, and tools not covered in the authors previous volume. This second volume focuses on inference in non- and semiparametric models. It not only reexamines the procedures introduced in the first volume from a more sophisticated point of view but also addresses new problems originating from the analysis of estimation of functions and other complex decision procedures and large-scale data analysis.

The book covers asymptotic efficiency in semiparametric models from the Le Cam and Fisherian points of view as well as some finite sample size optimality criteria based on Lehmann Scheffe theory. It develops the theory of semiparametric maximum likelihood estimation with applications to areas such as survival analysis. It also discusses methods of inference based on sieve models and asymptotic testing theory. The remainder of the book is devoted to model and variable selection, Monte Carlo methods, nonparametric curve estimation, and prediction, classification, and machine learning topics. The necessary background material is included in an appendix.

Using the tools and methods developed in this textbook, students will be ready for advanced research in modern statistics. Numerous examples illustrate statistical modeling and inference concepts while end-of-chapter problems reinforce elementary concepts and introduce important new topics. As in Volume I, measure theory is not required for understanding.

Check out Volume I for fundamental, classical statistical concepts leading to the material in this volume."

Recenzje

" . . . the authors have done a superb job of selecting topics comprising most of the essential knowledge needed formodern research. Furthermore, these modern topics are considered with greater depth and sophistication than is usual in a general purpose text. And throughout its pages the book does a good job of linking the mathematical developments to major examples. The choice of topics and examples, along with the depth of coverage are the most attractive features of this volume."
~RobertW. Keener, University of Michigan

Spis treści

Introduction and Examples. Tools for Asymptotic Analysis. Distribution-Free, Unbiased, and Equivariant Procedures. Inference in Semiparametric Models. Monte Carlo Methods. Nonparametric Inference for Functions of One Variable. Prediction and Machine Learning. Appendices. References. Indices.